Ministers have vowed to repeal a change to the Brexit bill imposed by the House of Lords after the Government was dealt its first major setback.
The Lords voted by 358 to 256 in favour of an opposition amendment for Theresa May to guarantee the rights of EU nationals in the UK after Brexit.
The Government described the result as "disappointing", but sources said they would try to reverse the result when the Bill returns to the House of Commons.
In the wake of the vote, opposing parties are urging ministers to reconsider their positions.
Labour's shadow Brexit secretary Sir Keir Starmer said: "There is a growing consensus this must be resolved before Article 50 is triggered, and the Prime Minister is now increasingly isolated."
However, there has been anger at the Lords' decision.
Labour MP Gisela Stuart, who co-chaired Vote Leave, said: "The British people voted in their millions to leave the EU, and their elected MPs passed the Article 50 Bill without amendment.
"The House of Lords should do the same and not seek to frustrate the Brexit process."
Despite the setback, ministers remain confident Mrs May's deadline for triggering Article 50 by the end of March will be met.
A spokesman for the Brexit Department said: "The Bill has a straightforward purpose - to enact the referendum result and allow the Government to get on with the negotiations."